Natural convection and thermal radiation analysis inside the square cavity filled with non-Newtonian fluid via heatlines and entropy generation

In the present analysis, natural convection heat transfer coupled with thermal radiation of bi-viscosity fluid contained inside the cavity has been studied through heatlines and entropy generation. Heat is provided to the cavity through heated source with length L/2, which is placed at the middle of bottom wall. Side walls of the enclosure at low temperature i.e. T_c ad rest of the walls are kept an adiabatic. The idea of Bejan heatlines and average Bejan number have been used to visualized the convective heat folw and dominant irreversibility due to fluid flow or heat transfer, respectively. Finite element method with penalty technique has been applied to obtain the solution of governing equations. Results are obtained through numerically and displayed in terms of streamlines, heat flux lines , isotherms, velocity, temperature, entropy, Nusselt number and average Bejan number against the extensive range of bi-viscosity β=0.002-1 and thermal radiation N_R=0-5, at fixed Rayleigh Ra=〖10〗^5 and Prandtl number Pr=10. It is observed that there exist a direct relation between bi-viscosity parameter and convection heat transfer due to buoyancy-driven flow. Moreover, the dominant entropy generation has been reported through heat transfer in the lower region of the cavity with and without thermal radiation.

Sparse STATIS-Dual via Elastic Net

Multi-set multivariate data analysis methods provide a way to analyze a series of tables together. In particular, the STATIS-dual method is applied in data tables where individuals can vary from one table to another, but the variables that are analyzed remain fixed. However, when you have a large number of variables or indicators, interpretation through traditional multiple-set methods is complex. For this reason, in this paper, a new methodology is proposed, which we have called Sparse STATIS-dual. This implements the elastic net penalty technique which seeks to retain the most important variables of the model and obtain more precise and interpretable results. As a complement to the new methodology and to materialize its application to data tables with fixed variables, a package is created in the R programming language, under the name Sparse STATIS-dual. Finally, an application to real data is presented and a comparison of results is made between the STATIS-dual and the Sparse STATIS-dual. The proposed method improves the informative capacity of the data and offers more easily interpretable solutions.

A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

Numerical Analysis of a Stable Discontinuous Galerkin Scheme for the Hydrostatic Stokes Problem

We propose a Discontinuous Galerkin (DG) scheme for the Hydrostatic Stokes equations. These equations, related to large-scale PDE models in Oceanography, are characterized by the loss of ellipticity of the vertical momentum equation. This fact provides some interesting challenges, such as the design of stable numerical schemes. The new scheme proposed here is based on the SIP penalty technique, with a particular treatment of the vertical velocity. It is well-known that stability of the mixed formulation of Primitive Equations requires, besides the LBB inf-sup condition, an additional hydrostatic inf-sup restriction relating pressure and vertical velocity. This hydrostatic inf-sup condition invalidates stability of usual Stokes stable continuous finite elements like Taylor-Hood 𝒫2/𝒫1 or bubble 𝒫1b/𝒫1. Here we prove stability for our 𝒫k/𝒫k DG scheme. Some novel numerical tests are provided which are in agreement with the previous analysis.

Line Search-Based Inverse Lithography Technique for Mask Design

As feature size is much smaller than the wavelength of illumination source of lithography equipments, resolution enhancement technology (RET) has been increasingly relied upon to minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this paper, we investigate the problem of pixelated binary mask design in a partially coherent imaging system. Similar to previous approaches, the mask design problem is formulated as a nonlinear program and is solved by gradient-based search. Our contributions are four novel techniques to achieve significantly better image quality. First, to transform the original bound-constrained formulation to an unconstrained optimization problem, we propose a new noncyclic transformation of mask variables to replace the wellknown cyclic one. As our transformation is monotonic, it enables a better control in flipping pixels. Second, based on this new transformation, we propose a highly efficient line search-based heuristic technique to solve the resulting unconstrained optimization. Third, to simplify the optimization, instead of using discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Forth, we introduce a jump technique in order to jump out of local minimum and continue the search.

Adaptive Wavelet Method for Incompressible Flows in Complex Domains

An adaptive wavelet-based method provides an alternative means to refine grids according to local demands of the physical solution. One of the prominent challenges of such a method is the application to problems defined on complex domains. In the case of incompressible flow, the application to problems with complicated domains is made possible by the use of the Navier-Stokes–Brinkman equations. These equations take into account solid obstacles by adding a penalized velocity term in the momentum equation. In this study, an adaptive wavelet collocation method, based on interpolating wavelets, is first applied to a benchmark problem defined on a simple domain to demonstrate the accuracy and efficiency of the method. Then the penalty technique is used to simulate flows over obstacles. The numerical results are compared to those obtained by other computational approaches as well as to experiments.